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DanielLC comments on Diplomacy as a Game Theory Laboratory - Less Wrong
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You could roll the die so everyone else can't see them, then take a picture with your cell-phone. At the end, you can prove that you were doing what the die said.
Nothing could stop you from rolling the die until you get the wanted number, and then only publishing one result.
To be credible, you'd need a RNG that you can't use without everyone else knowing that you did (if not the specific result), which usually means a third party.
Online D&D uses trusted die-roller websites that keep logs of all the rolls made under one's name; you could have a variant where they just publish a hash of the results, rather than the results themselves.